| (fac(i - j) * j * fac(j - 1)) * i0 = fac(i), fac(i) = fac(j - 1) * (i + 1 - j) * fac(i - j) * i1, 0 < j, 0 ≤ i, 0 ≤ j, 0 < i, j ≤ i ⊦ i0 * j = i1 * (i + 1 - j) |
(fac(i - j) * j * fac(j - 1)) * i0 = fac(i), (fac(i - j) * j * fac(j - 1)) * i0 = fac(j - 1) * (i + 1 - j) * fac(i - j) * i1, 0 < j, 0 ≤ i, 0 ≤ j, 0 < i, j ≤ i ⊦ i0 * j = i1 * (i + 1 - j)